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Geometry, Physics, and Symmetries

Group “Fundamental Interactions”

Our activities are centered on the mathematical description of physical laws, in particular laws that govern fundamental interactions. The necessary tools are often of geometric, algebraic, combinatorial, analytic or functional nature. Some results or problems lead to the emergence of new mathematical structures needing a dedicated study. Others have direct physical applications.

Fundamental laws of nature, at the classical level, are naturally expressed in terms of geometry (for instance the notion of connection on a bundle appears in our understanding of both gravity and strong or electroweak interactions), and symmetries of the physical world are usually described, classically, by group theoretical constructions, in particular representation theory. Geometry finds its roots in the study of symmetries but one knows that mechanics itself uses geometry, in particular symplectic geometry, for its own formulation. A quantum description of physics requires not only the above tools but also appropriate generalizations of these notions. Approaches leading to theories of quantum gravity using non-commutative geometry, for instance, need mathematical descriptions where space-time (actually its algebra of functions) is replaced by a non-commutative algebra; moreover many developments of quantum field theory use generalizations of the notion of group, for instance supersymmetric theories use Lie super-algebras, and conformal field theory or string theory, as well as the theory of integrable systems, use concepts coming from affine Lie algebras and quantum groups.
Our activities focus around the above themes.

Directory of Members

Attard Jérémy PhD candidate
Email
Bizi Nadir PhD candidate
Email
BULGAKOVA Daria PhD candidate
Email
Coquereaux Robert Researcher
+33.4.91.26.95.18 Email
Duval Christian Emeritus
+33.4.91.26.97.97 Email
Giovannetti Gabriel ATER
Email
Iochum Bruno Emeritus
+33.4.91.26.97.96 Email
Krajewski Thomas University faculty
+33.4.91.26.95.61 Email
Lazzarini Serge University faculty
Chef de l’équipe « Géométrie, Physique et Symétries »
Web editor
Correspondant FRUMAM
+33.4.91.26.97.94 Email
Luminet Jean-Pierre Guest
+33.4.91.26.95.19 Email
Marsot Loïc PhD candidate
Email
Masson Thierry Researcher
Communications manager
Correspondant valorisation
+33.4.91.26.97.94 Email
Ogievetsky Oleg University faculty
+33.4.91.26.95.33 Email
Schücker Thomas University faculty
Chef du Groupe « Interactions fondamentales »
+33.4.91.26.95.61 Email
Triay Roland University faculty
+33.4.91.26.95.19 Email

List of Publications

97 results
Conference paper
Robert Coquereaux
Character tables (modular data) for Drinfeld doubles of finite groups
7th International Conference on Mathematical Methods in Physics, Apr 2012, Rio de Janeiro, Brazil. http://pos.sissa.it/archive/conferences/175/024/ICMP%202012_024.pdf, pp.PoS(ICMP 2012)024, 2012
Journal article
B. Iochum, T. Masson, A. Sitarz
$\kappa$-deformation, affine group and spectral triples
Banach Center Publications, Institute of Mathematics Polish Academy of Sciences, 2012, 98, pp.261--291. 〈10.4064/bc98-0-11〉
Book Section
Thierry Masson
Gauge theories in noncommutative geometry
Joseph Kouneiher Cécile Barbachoux Thierry Masson and Dimitry Vey. Frontiers of Fundamental Physics: The Eleventh International Symposium, AIP, pp.73, 2012, AIP Conference Proceedings
Journal article
Serge Lazzarini, Thierry Masson
Connections on Lie algebroids and on derivation-based noncommutative geometry
Journal of Geometry and Physics, Elsevier, 2012, 62, pp.387-402. 〈10.1016/j.geomphys.2011.11.002〉
Preprint, Working paper
Cédric Fournel, Serge Lazzarini, Thierry Masson
Local description of generalized forms on transitive Lie algebroids and applications
2011
Journal article
Christian Duval, Peter Horvathy
Conformal Galilei groups, Veronese curves, and Newton-Hooke spacetimes
Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2011, 44, 335203 (21pp). 〈10.1088/1751-8113/44/33/335203〉
Journal article
Christian Duval, Galliano Valent
A new integrable system on the sphere and conformally equivariant quantization
Journal of Geometry and Physics, Elsevier, 2011, 61 (1), pp.1329-1347. 〈10.1016/j.geomphys.2011.02.020〉
Journal article
Bruno Iochum, Thierry Masson, Thomas Schucker, Andrzej Sitarz
$\kappa$-Deformation and Spectral Triples
Acta Physica Polonica B, Jagellonian University, Cracow, 2011, 4 (3), pp.305. 〈10.5506/APhysPolBSupp.4.305〉
Journal article
Bruno Iochum, Thierry Masson, Thomas Schücker, Andrzej Sitarz
Compact $\kappa$-deformation and spectral triples
Reports on Mathematical Physics, Elsevier, 2011, 68 (1), pp.37-64
Preprint, Working paper
Thomas Schucker
Lensing in the Einstein-Straus solution
2011
97 results

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